DESCRIPTION (Adapted from Investigator's Abstract) The major objective of this proposed research is to develop statistical methods for analyzing survival times and failure rates from data that contain correlated responses. An assumption of uncorrelated responses is the basis for the most commonly used survival models, but correlated responses cannot be avoided in many health studies for reasons such as: (1) genetic relationships among respondents, e.g. occurrence of breast cancer for sets of sisters or occurrence of tumors in mice from the same litter; (2) social and psychological relationships, e.g. in some smoking cessation programs participants are treated in groups that can include spouses, relatives, and friends who are encouraged to provide support for each other; (3) simultaneously monitoring times to occurrence of several different life events for each subject in the study, e.g. the times to development of several different traits may be monitored for each subject or test animal exposed to a carcinogen. Failure to properly incorporate such correlations into the analysis of survival data can have serious consequences. The investigators state that applying treatments to subjects within groups of positively correlated subjects can improve the precision of treatment comparisons allowing sample sizes to be reduced. Conversely, ignoring the correlations when treatments are applied across groups of correlated subjects leads to overstating the significance of treatment effects. Three basic approaches are to be developed: (1) a semiparametric approach based on an extension of a proportional hazards model to correlated survival data, (2) a parametric model of constructing multivariate distributions with specific marginal distributions, (3) an extension of a bootstrap method for analyzing correlated survival data that does not require an explicit model for the correlations. The accuracy and efficiency of methods of parameter estimation and inference are to be examined for each of the three approaches with the analysis of data obtained from recent human health studies and also with computer simulations. User friendly and portable computer programs are to be developed with either the FORTRAN or C programing languages to facilitate applications of these statistical procedures in human health research. The stability, accuracy, and efficiency of the proposed computer software are to be thoroughly evaluated.